In his entry on "Weights and Measures" in the Encyclopaedia Britannica (1911), Flinders Petrie claims that "the Belgic foot of the Tungri is the basis of the present English land measures, which we thus see are neither Roman nor British in origin, but Belgic." (1) Land measures still in use today, from the rod to the mile, were once expressed in terms of multiples of a different foot to the one we have today. He then goes on to say of the Belgic foot:

It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system. Had it not been unhappily driven out by the 12-in. foot, and repressed by statutes both against its yard and mile, we should need but a small change to place our measures in accord with the metre. (2)

Surprisingly, according to Flinders Petrie, Britain, and northern Europe, once had a *decimal* system of measure (as opposed to the duodecimal imperial system, based on the number twelve), with a unit close in size to the modern metre.

## 1. History of the Belgic Foot

Flinders Petrie doesn't state what he believes the Belgic foot to measure exactly, but he equates it to a measure of close to 13.3 inches or 13.22 inches. If today's value for the metre, 39.3700787402 inches, were considered a yard of three feet, then the foot would be 13.12336 inches long. However, Flinders Petrie used a slightly different metric-imperial ratio, writing in 1911. In this same article for the Encyclopaedia Britannica, he gives 39.37 inches for the metre in the United States and 39.3700113 inches in Great Britain, which would yield a slightly shorter foot of 13.12334 inches.

What remains of the predecessor of the imperial system in Britain is indeed decimal: a mile is 8 furlongs, but was once 10 furlongs. A furlong is 10 chains, a chain is 10 fathoms. 400 feet of 13.2 inches fit into a mile, and this foot of 13.2 inches gives a yard of 39.6 inches, which is 54 x 0.733333 inches. A unit of about 40 inches was in use, called the yard and full hand, and a third of that would have been 13¹/³ inches.

Flinders Petrie explains:

Turning now to England, we find the commonest building foot up to the 15th century averaged 13·22. Here we see the Belgic foot passed over to England, and we can fill the gap to a considerable extent from the itinerary measures. It has been shown that the old English mile, at least as far back as the 13th century, was of 10 and not 8 furlongs. It was therefore equal to 79,200 in., and divided decimally into 10 furlongs, 100 chains, or 1000 fathoms. For the existence of this fathom (half the Belgic pertica) we have the proof of its half, or yard, needing to be suppressed by statute (9) in 1439, as “the yard and full hand,” or about 40 in.,—evidently the yard of the most usual old English foot of 13·22, which would be 39·66. We can restore then the old English system of long measure from the buildings, the statute-prohibition, the surviving chain and furlong, and the old English mile shown by maps and itineraries, thus:—

foot, 3＝yard, 2＝fathom, 10＝chain,10＝furlong,10＝mile

13·22 39·66 79·32 793.2 7932 79,320

Such a regular and extensive system could not have been put into use throughout the whole country suddenly in 1250, especially as it must have had to resist the legal foot now in use, which was enforced (9) as early as 950. We cannot suppose that such a system would be invented and become general in face of the laws enforcing the 12-in. foot. Therefore it must be dated some time before the 10th century, and this brings it as near as we can now hope to the Belgic foot, which lasted certainly to the 3rd or 4th century, and is exactly in the line of migration of the Belgic tribes into Britain. (3)

Flinders Petrie goes on to say:

13·3.—This measure does not seem to belong to very early times, and it may probably have originated in Asia Minor. It is found there as 13·35 in buildings. Hultsch gives it rather less, at 13·1, as the “small Asiatic foot.” Thence it passed to Greece, where it is found (25) as 13·36. In Romano-African remains it is often found, rather higher, or 13·45 average (25). It lasted in Asia apparently till the building of the palace at Mashita (A.D. 620), where it is 13·22, according to the rough measures we have (25). And it may well be the origin of the diráʽ Starabuli of 26·6, twice 13·3. Found in Asia Minor and northern Greece, it does not appear unreasonable to connect it, as Hultsch does, with the Belgic foot of the Tungri, which was legalized (or perhaps introduced) by Drusus when governor, as 1/8 longer than the Roman foot, or 13·07; this statement was evidently an approximation by an increase of 2 digits, so that the small difference from 13·3 is not worth notice. Further, the pertica was 12 ft. of 18 digits,i.e.Drusian feet. (4)

The Belgic foot here is equated with the Drusian foot, and compared to lengths found in Asia and Africa. Flinders Petrie compares measures from between 13.07 and 13.45 inches and groups them together as connected to the Drusian foot. It is seen as a cousin of the 11.664 inch or 11.666 inch Roman foot of sixteen digits, being eighteen of these same digits of 0.729 or 0.729166667 inches. Eighteen digits of 0.729 inches are 13.122 inches, and eighteen digits of 0.729166667 inches are 13.125 inches. Flinders Petrie gives the Drusian foot as 13.07 inches, or at least a Roman foot + 1/8 of a Roman foot. So that would mean 13.122 inches for a Roman foot of 11.664. Fifty four digits of 0.729 inches give a yard or metre of 39.366 inches, fifty four digits of 0.733333 inches give a metre of 39.6 inches, and fifty four of the 0.729166667 inch digit give 39.375 inches. The pertica, 12 feet of 18 digits, or 12 Drusian feet, as Flinders Petrie suggests, would also work out at around 4 metres. In fact, it would be very close to 4 metres of the types Berriman mentions in *Historical Metrology*, of 54 digits of 0.729 inches being 39.366 inches, or of 54 digits o 0.7291666667 inches being 39.375 inches.

Flinders Petrie refers to Hultsch, who writes about the "Tungri foot of Drusius"(*Tungris pes*

*Drusianus*). This small Asiatic foot is 335 millimeters, he writes, according to research by Fenneberg. He mentions a stadium length of 207.5 metres found in a French archaeological book, from which he derives a foot of 332 millimetres. This is an interesting measure too, as 207.5 metres multiplied by Phi, the golden ratio, and divided by 1,000, is 335.7418 millimetres, or 13.21816 inches.

John Neal agrees with Flinders Petrie that the Belgic foot is one third of a metre, "commonly known as, a Belgic foot, i.e. nine to eight of the Roman foot, as established by Nero Claudius Drusus, the Roman governor of Gaul." (6) Neal also adds a new aspect to the question: the polar circumference of the earth and its divisions along lines of latitude, "what I term the Root Geographic Belgic foot; of which there are 333333.333 to the meridian degree at 38 degrees."Neal also writes: "many modules attributed to different cultures are in fact variations of the same basic foot, such as Saxon and Sumerian."However, he warns: "Metrologists continually confuse the Belgic, Frankish and Saxon/Sumerian, the latter has also been appended Ptolemaic. But, the differences become distinctively identifiable at the lengths of the *pertica, chain, furlong, stadium, mile* etc.."(7) There is some confusion around this topic, as the measures of all these units are very close. Furthermore, it is generally accepted that many ancient units of measure have variations, either due to historical changes, or to questions of geometry, with a unit relating to another as parts of a shape, or to the latitude where the unit was in use. Neal gives 1.071428 feet, i.e.12.857136 inches to the Belgic foot, which he says then "develops into the Drusian foot or foot of the Tungri" and is "detectable in many Megalithic monuments."(7)

1.071428 feet is 7.5 / 7 feet, or 90 / 7 inches, or 16/49 metres (of 39.375 inches).

Another historian of metrology, writing in 1756, Fréret, writes:

This same Hygin still mentions another foot in Hygiu. ibid, usage among the Romans, & employed outside Italy for the 210. measurement of land. He calls it the foot of Drusus, and says that it contained 13 and a half inches of the Roman foot, that is to say 27 half-inches. This foot of Drusus was that which had been used to measure the lands of the country of Tongres, distributed to the Roman soldiers in lower Germany.

(...)

With regard to the measurement of the mile given by Heron, as by the preceding hypothesis, it supposes that the foot of this mile contained 27 half-inches of the Roman foot, and that it was the same as the foot of Drusus determined by Hygin; it must be established that the mile of which Heron speaks is that which had been used by Augustus to regulate the military routes, the march of the troops, the places of residence and the stages in Egypt: all this having been done during the reign of Augustus, it is very likely that the foot of Drusus was used, which seems to have been used then in matters pertaining to military discipline.

Fréret also writes:

The foot which Hygin calls the foot of Drusus, and which he says was in use in Germany and in the country of Tongeren, contained twenty-seven and twenty-fourths [27/24] of the Roman foot, that is to say 13 inches, so that it contained nine eighths. Taking the Roman foot of Statilius of 1312 tenths, the foot of Drusus will have 1476 tenths, or 36 tenths more than the foot of France. If we take one of the Roman feet less than that of Statilius, for example, that of 1296, given by the measurement of the first three feet of iron examined by Luca Petto, the foot of Drusus will have 1458 1/3, or nearly two lines more than thepied du roi.

In the office of the Elector Palatine, in the time of Freherus, there was kept a rod of square iron on which were read these words in silver characters: CARLVS. PRINT. JVSSIT CVBITV IST FACERE JVXTA MENSVRAM SVAM. This measure contains 6 feet & 3 inches from the Leid or Rhineland foot; this foot contains 1392 tenths of a line, according to the measurement taken by M. Picard (c), during his trip to Uranibourg, that is to say two lines more than he had given him at first. The sixth part of this rod of iron therefore contains 1450 tenths of a line, that is to say, taking it for a fathom or measure of 6 feet, the foot will have 1450 tenths, that is to say: 8/10 lines less the foot of Drusus. As we have found in Rome iron feet that are even shorter than that of 1296, if we look at this measurement of the cabinet of the Palatine Elector as the toise or pertica of the foot of Drusus, the size of this foot will have been determined by Hygin on a Roman foot of 1289 tenths only, & shorter by half a line than that of 1295, measured by Luca Pettò in the Delfini study.

11.664 x 27/24 = 11.664 x 9/8 = 13.122

11.666667x 27/24 = 11.666667 x 9/8 = 13.12511.6666

1 toise came to be valued at 1949.03631 mm, with the advent of the metre. So 1 line would have been worth 1949.03631 / 864 = 2.2558290625, and one tenth of a line 0.22558290625 mm. So for example when Fréret describes Rhineland foot; this foot contains 1392 tenths of a line, this can tentatively be converted into millimetres as 314.0114055. In fact it is possible that 1 Rhineland foot could have been the length of the circumference on a diameter of 100 mm approximately, or that 1 toise of 6 feet, each worth 33.333 cm, or 13.125", more or less, a Druisian foot, would have a circumference of 20 Rhineland feet, each of 314.15927 mm approximately. In fact, if Fréret's measure for the Rhineland foot is taken to be 314.0114055 mm exactly, and with calculator pi, the foot on the diameter of the circle would be 333.176449 mm long. or 13.117", or 13118".

6 feet & 3 inches of the Rhineland foot would make up 314.0114055 x 6 + 314.0114055/12 x 3 = 1,962.571284375 mm (approx. 77.27624"). This is the length given of the iron rod in the office of the Elector Palatine, in the time of Freherus, or 6 x 1450 tenths of a line, around 327.095214 mm, or 12.87776". This is equated by Fréret to the foot of Drusus, being a sixth part of the Palatine Elector iron rod. This is quite a bit shorter than expected, but then again, so are all his measures of the Roman foot. Fréret is working with lines, and tenths of line, of the pied du roi that existed in 1756, and with a measure of the Roman foot taken from the tomb of Statilius. (see Fréret p__ 490__) He considers various lengths for the Drusian foot: if the Roman foot of Statilius is 1312 tenths [of a line of the foot] , the Drusian foot will be 1476 tenths, or 36 tenths more than the "pied de France". Or taking 1296 1/3 , which is the measure of the three feet examined by Luca Petto , the Drusian foot is 1458 1/3 , or almost two lines more than the *pied de Roi* . If a line was worth 2.255829 mm, then two would have been 4.511658 mm. One pied de roi would have been worth 1949.03631 / 6 = 324.839385 mm. If that corresponded to 144 lines, 146 lines would have been 329.35104312 mm.

The Rhineland foot Fréret refers to is the Rijnlandse Roede, or Rhenish Rod, is in Leiden, and was once the old standard of unit of length for the Dutch Empire. The metal rod is exactly 1 Rhenish foot long. It was precisely determined by Christiaan Huygens and Willebrord Snellius who used it in their work. Huygens used the rod in his pendulum clocks, and Snell expressed the diameter of the earth in it. Curiously, the Rhenish foot is 0.3140 metres (divided into 12 Rhenish thumbs). this is close to pi/10. However, in 1807, de Gelder measured the copy of the Rijnland foot in the Leiden observatory, and got a measure of 0.3139465 m. This is close to the Prussian foot of 0.3138 metres and the Danish foot of 0.3139 metres.

Perhaps there is no historical connection to pi, or to the metre. However, it is an interesting possibility that some kind of proto metre, long before the French revolution, was used as a geometrical basis for the foot of the Rhineland. The connection to the geometry of a circle can also simply be explained by the Belgic foot, that is close to a third of a modern metre in length. Wim Verhart has offered a good alternative to the origin of the Rhineland foot:

The Swedish Foot was 0.2960 meters. Multiplied by 1.5 we obtain 0.444 Divided by the root of 2 we obtain 0.313955 meters. This is even a better approximation for the Rends Vote of Leiden.

There is some confusion in the historical and geographic connections. The Belgae, though they gave their name to modern Belgium, were tribes living across a large area, in what is now northern France, all the way from the river Seine to the borders with Germania, from at least the third century BC. The Tungri seem to have been a tribe living within this Belgic part of Gaul in Roman times, yet they were also described by Tacitus as being called the first "*Germani*". All the tribes living east of the river Rhine, well into modern Germany, were also named after them. So it seems the Belgic or Tungri foot could have been present in what is now northern France, Belgium, and Germany, and possibly beyond. In fact the Belgic foot is very similar in size to the northern or Saxon foot. It's also possible that tribes in Great Britain were also Belgae, or were conquered by them, in the late sixth or early fifth century BC. Those known as *Iverni *went to Ireland, which gave the name Hibernia, land of winter. In the Irish history written long ago, they may be remembered as the* Fir Bolg*, *fir* meaning *men*, who were responsible for dividing Ireland into five provinces. The connection to the Belgae is uncertain, and it is said quite clearly in the Irish *Book of Invasions *that the reason for this name, Bolg, was because these men carried bags, and no mention of the Belgae as a people is made. (5) The Fir Bolg may have come from much farther afield, as one of their queens, Tailltiu, was the daughter of Mag Mór, the king of Spain, and they also had a connection to Greece. The tendency to view pre-modern history as largely travel-free isn't corroborated neither by fact or myth.

## 2. The Northern or Saxon foot, the Babylonian foot and the Indus Valley foot

So what is this Saxon or Sumerian foot, which John Neal warned us against confusing with a Belgic foot? Berriman gives the value of the Sumerian foot as 13.2 inches, which fits exactly 400 times into the imperial mile, and 5/4 times into a rod or pole of 16.5 imperial feet. For Neal, the Belgic foot is 1.071428 English feet, and "develops into the Drusian foot or foot of the Tungri. Detectable in many Megalithic monuments." The Sumerian foot is 1.097142 English feet, or 92.16 / 7 inches, which is 12² x 4³ / 700 = 13.16571429 inches. Neal adds that it is "perhaps the most widely dispersed module of all, recorded throughout Europe, Asia and North Africa, commonly known as the Saxon or Northern foot."

Jim Wakefield gives the same value of 13.2 inches for the "Saxon or Drusian foot", equating the Drusian foot to the Saxon foot, not the Belgic, as Neal has done. Whatever name is given to it, this length of 13.2", and variations on this between roughly 13.1 and 13.33 inches, have been important in many parts of the world. Skinner also defined the Saxon oot as 13.2 inches, and believes the foot entered Britain only long after the fall of the Roman Empire:

The Saxon foot was derived from a very ancient and wide spread measure known as the Northern Cubit, a non-Semitic standard varying between 26" and 27" which can be traced in building work, and as actual Cubit Measures in Mesopotamia and Egypt from about B.C. 2000 and which was always associated with land measure. This cubit and its half or foot passed westwards into Europe with the early migrations from the east of the Teutonic tribes. In B.C. 12, this foot was recognised as the standard for land measurement among the tribes of Lower Germany and its length was recorded by the Roman general Drusus as " 2 digiti longer than the Roman Pes " (foot), i.e. a length of 13-11". After A.D. 410 with the departure of the Romans and the coming of the Saxons, the Northern Cubit and Foot became established in England in the Saxon kingdoms at a value of 264" for the Cubit or Ell as a cloth measure and a foot of 13'2" for building, and for land measure for their " Open Field " system of ploughlands, in which the various " holdings " were rectangular strips side by side, known as " Roods " (1/4 acres). (11)

Jim Wakfield has written about the Saxon foot in a paper called "From the Rollrights to Stonehenge" as a measure with an ancient origin, as Skinner says, but which is found in Britain long before the Romans. This unit has been found in meaningful quantities at megalithic stone circles.

There is evidence that the Saxon foot of 13.2 inches was used in Britain in the neolithic, and while this doesn't disprove the theory that it came from the Middle East originally, it opens the question of origin.

The variations on this measure such as 13.2 and 13.125 could simply be the product of different pi values. 13.125 x 8/25 x 22/7 = 13.2 . 13.122 and 13.125 are separated by the 4374/4375 ratio (ragisma).

The history of measures is one way to see just how far people did travel. Indeed, the Northern or Saxon foot may be considered essentially the same as the Sumerian foot. This view is put forward by Berriman, who gives the Sumerian foot a value of 13.2 inches or 335 mm. The Sumerian cubit, 19.8 inches or 502 mm according to Berriman, is also one tenth of the English rod or pole of 16.5 feet. It's also the half sacred Jewish cubit that interested Newton. One tenth of 16.5 feet (a rod) is also close to 16 x π /100 metres, or 8/5 x π metres.

Jim Alison regards the Northern or Saxon foot, the Babylonian foot and the Indus Valley foot as the same.

Neal links the Greek foot with the English measures, with a value of 1.028571 feet. This value allows an interesting comparison to be made between the Greek and English feet: the Greek foot is 72 / 70 English feet, or 864 / 70 inches, or 25,920 / 2,100 inches. and the English foot is 72 / 72 English feet. Berriman has a theoretical unit of 1.296 inches, ten of which make an Assyrian foot. The Greek foot as 72/70 English feet is also 1296 / 105 inches, and the English foot 1296 / 108 inches. The Assyrian foot is 8/9 of a remen of 14.58 inches, according to Berriman. The Greek foot is therefore a remen of 14.58 inches multiplied by 800/945 inches, or 1,000 Roman / Egyptian feet of 11.664 inches divided by 945. The English foot itself is the remen multiplied by 800 / 972, or 1,000 Egyptian / Roman foot divided by 972. The foot of 18 Roman / Egyptian digits (call it Saxon, Sumerian, Northern, Belgic, Drusian, or other), is therefore the Greek foot multiplied by 945 x 18 / 16,000, giving a value of 13.122 inches.

Neal describes the Greek foot as "a very widely used module recorded throughout Europe, it survived in England at least until the reforms of Edward I in 1305. It is also the half sacred Jewish cubit upon which Newton pondered and Berriman referred to as cubit A."Half of Berriman's cubit A, which Berriman defines as 2/π metres, is 12.53 inches, which is a little shorter than 18 Roman / Egyptian digits. This value of 12.53 inches relates more easily to the Egyptian Royal cubit than it does to the digit or remen. A Neal / Michell Egyptian royal cubit of 20.618181818 inches being a metres x 2/10 x 55/144, so this cubit A is the Egyptian royal cubit multiplied by 55/144 x 10/2 x 1/π, or more simply, by 25/6 x (55/144)² .

Flinders Petrie writes that the Belgic or Drusian foot came to be superseded in England and was repalced by the imperial system we have today. But some aspects of the older system live on in the larger units, conncted to land measurement. the rod, for example, measures 16.5 feet, or 5.5 yards, or 198 inches, which are in fact 15 Northern or Saxon feet. And indeed 198 inches / 15 = 13.2 inches

## 3. Metric connections

Jim Wakefield describes the metrological tradition that gave us the 13.2" foot, or thereabounce, as "a wonderful system of measures as it includes a metric system nearly the duplicate of the present metric system but managing to incorporate both the metric and imperial system magnificently". This echoes Flinders Petrie's view in his Encyclopaedia article:

It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system. Had it not been unhappily driven out by the 12-in. foot, and repressed by statutes both against its yard and mile, we should need but a small change to place our measures in accord with the metre.

In *Carnac, The Alignments* book (Vol 1), Howard Crowhurst says on page 15 that the Drusian or Teutonic feet "were found to measure exactly 333 millimetres from the 13th century". He mentions this in the context of "the exact conversion between megalithic yards and metres", 63 metres being 76 megalithic yards.

Mauss writes about a Persian foot of 330 mm ( and another of 350 mm), and compares this to the size of tiles found in the south of France from the 10th century which measure 33cm. He suggests that a similar 329.142 mm length could in fact be half a Persian / Assyrian royal cubit of 658.285 mm (that is, 4,608 / 7 mm), or 25.92 inches. The Newton Sacred Cubit of 12 x 12 x 12 x 12 x 12 /10,000 inches. 25.92 is 12 x 12 x 12 x 15 / 1,000 inches.

Neal, on page 292 of his *Ancient Metrology*, in the chapter called Chinese Metrology, gives some lengths for the foot "Suggested by the Register of Cun Lengths", working off some measures taken in millimetres. He lists 250 mm as equivalent to 3/4 of the Sumerian foot. This seems to mean that for Neal, the Sumerian foot is a third of an ancient metre. Neal ends his preamble to the book with the words "the damn metric system", and yet finishes the book leaving us hanging in suspense with these connections to the millimetre.

__Jim Alison__ has put forward a value of 0.333 m for the length of "the Babylonian foot, the Indus Valley foot and the old Northern foot, and two and a half of these feet for the length of the megalithic yard."Jim Alison shows clearly the links between the ancient Babylonian system and the modern metric system:

The Babylonian foot contains 20 shusi, or one-third of one meter. The Babylonian cubit contains 30 shusi, or one-half of one meter, and the double cubit contains 60 shusi, or one meter. The weight of the Babylonian mina is 500 grams. The weight of the Babylonian talent is 60 mina and the weight of the Babylonian shekel is 1/60th of one mina. The cuneiform inscription on British Museum exhibit number 91148 gives a weight of two mina during the reign of Shulgi, (c. 2000 B.C.) This weight is 1000 grams, or 500 grams per mina.10

Recently, an article dealing with some interesting acrachological finds in Mâcon in France, by Daniel Barthèlemy and Stéphane Dubois, backed up this link between an ancient foot and the metre. It's about a metal ruler, from Roman times, broken on one end, but with the markings clearly legible. The authors of the article think it's closest to Hultsch's Druisian foot of 33.27cm, or at least half of one. An inch of a Hultsch Druisian foot would measure 2.77 cm. The half inch on this metal rod measures 1.39 cm, which would give an inch of 2.78 cm (or 1.094488189").

A digit of 0.72916667" multiplied by 1.5 gives 1.09375", or 2.778125 cm. Could this be the intended value, rather than 2.78 cm? 12 of these 'half inches' of 1.09375" (or 2.778125 modern cm) would give 13.125", or 33.3375 modern cm, or 100 / 3 'ancient' cm, from the 39.375" metre. So 36 Mâcon inches are 1 ancient metre. 16 Mâcon inches would give 17.5" or 44.45 cm, or 400 / 9 ancient cm. 27 give 29.53125" or 75.009375 cm, or 75 ancient cm.

And 9 would give 27 x 0.36458333" = 9.84375" = 25.003125 modern cm = 25 'ancient' cm (cm of the 39.375" metre). The 2.78 cm inch as per the article could perhaps be 2.778125 cm or 2.77777 cm.

The Mâcon ruler has a half inch which measures 1.39 cm according to the authors. This could be compatible with the ancient metre and with the 0.729166667" digit. The Mâcon inch would be half of 2.778125 cm, or half of 0.729166667" x 1.5. So one Mâcon inch = 0.729166667" x 3/2.

In a blog post on GHMB, Jim Alison observed that"Two fifths of a Mâcon inch are 40/36 x 8,001/8000 cm, which suggests 1/10,000,000th of a degree of latitude of a 1,575,000,000" or 40,000,000 ancient metre circumference. Meanwhile, 1/3 m, divided by 12 = 2.777... cm for the inch, or divided by 2 = 1.3888... cm for the half inch. If we correct for the 5001/5000 error in the meter, then 1.3888... x 5001/5000 = 1.3891666... cm In any event, this ruler gives a value very close to 1/3 m for the Northern foot, so in comparison to 40,000,000 m in the polar circumference, this gives 120,000,000 Northern feet for the polar circumference."

"A new look at the astronomy and geometry of Stonehenge" by Euan MacKie

Two of the several new inferences made are of particular interest to this essay. The first is one result of a statistical analysis of the various measurements collected, which showed that a unit of length of 0.665m – or two of these making 1.33m – could have been used. Ranieri thought this was probably of little general importance but was evidently unaware that these lengths are multiples of the Drusian or ‘Northern’ foot of 0.333 m which survived in England into Saxon times when it was used in the dimensions of some religious buildings.

It is intriguing that this unit fits the ‘ideal’ dimensions of the Station Stone Rectangle slightly better than does the megalithic yard(see Table in Appendix). The sides of the Station Stones triangle then become 100, 240 and 260 Drusian feet. The second new inference was that the point on the main axis of the site, where it passes through the gap between the Heel stone and its vanished companion on its northwest side, appears to be connected geometrically to the Station Stone Rectangle (Figure 3). If the line between stone 92 and 93 is regarded as the base of two opposed right-angled triangles – the upright sides of which are the site axis (Figure 3),and the apices of which are at the Heel stone point just mentioned – then these too are in the proportions of 5, 12 and 13. Here, however, the megalithic yard does not work (see Table in the Appendix) because two sides of the triangle have to be in fractions, namely 48, 115.2 and 124.8. In terms of the Drusian foot, however, they are 120, 288 and 312, which supports the idea that this was the unit of measure used in early Stonehenge.

This 'Druisian' foot, of 0.333 metres, fits in well, as MacKie says. The terminology is a bit confusing, as it's close to being a third of an ancient metre, or 13.125". Over a few pints on Lundy, Neal, Michell and Heath came to the conclusion that a "unit of two Druisian feet defines the station stone rectangle at Stonehenge, with its diagonal, as 50:120:130, decimally matching the 5:12:13 proportion. The short sides become 100 Druisian feet in length."

The value of *this* Druisian foot is 15/14ths of the English foot, then converted to "Geographic" from "Root", so multiplied by 3168/3125, which gives 1.08617143 feet, which works out at 0.33107 metres. (see page 52, in *Lost Science*) It's not quite the Druisian foot from MacKie's table anyway.

If you take the dimensions between stones 91 and 92, given here as 34.17 metres, convert it to miles and multiply by the lunar year in days, and divide by the solar year in days, that's 206/10,000 miles. Saint Michael's Mount - Mont Saint-Michel is 206.14 miles, centre to centre.

Jim Wakefield has observed:

Acre 43560 imperial feet squared.

Acre 36000 Saxon foot squared.

Saxon foot 13.2 inches.

GP connection.

43560 - 36000 = 7560

Cos 7560 = 1

Cos 756 = 0.809016994 X 2 = 1.618033989

This refers to a discovery of Derek Skane's, that cos 756 is Phi.

Newton wrote:

TheTalmudistswrite, that the height of the steps, by which they ascended to the inner court, was half a Cubit, and their retractions half a Cubit. They mean the sacred Cubit; and we see thatJosephus's computation, with regard to the height of these steps, corresponds with them. NowVitruviusdetermines, that the height of steps ought not to be more than 10Roman Unciæ, and the retractions not less than 18Unciæ; when, since theJewsmake the height equal to the retractions, we must suppose that they took a middle proportion, and that the height, as well as the retractions, made about 12, or at most 13Roman Unciæ. The middle proportion between 10 and 18 is about 13⁵/¹². And I should be inclined to maintain, that this height was not at all exceeded, lest it might have been difficult to ascend the steps. The sacred Cubit therefore was less than 27Roman Unciæ, but not less than 24Unciæ, in order that the retractions of the steps might not be too much lessen'd.

(...)

TheRomanCubit therefore consists of 18Unciæ, and the sacred Cubit of 25³/⁵Unciæof theRomanFoot; and consequently those Cubits are to each other in round numbers as 2 to 3 very near. And this proportion is used byJosephus, out of regard to the greater expedition in computing the bulk of the buildings. For writing to theRomans(g)[7], he every where puts threeRomanCubits for about two sacred Cubits

As Newton suggests 11.664 / 12 x 18 = 17.496 inches, this is the Roman cubit. And the sacred cubitis then 11.664 / 12 x 25 ³/⁵ = 24.8832. This is suprising as it's 12⁵ /10,000 imperial inches. I am not sure why Newton doesn't point this out, but it suggests that the origin of the English or imperial inch is linked to the sacred cubit that Newton writes about.

But Neal suggests other value for sacred cubit of Newton's: 24.68568 inches:

Common Greek1.028571ft— This was a very widely used module recorded throughout Europe, it survived in England at least until the reforms of Edward I in 1305. It is also the half sacred Jewish cubit upon which Newton pondered and Berriman referred to as cubit A.

Also, I'm not sure where he gets his value for Berriman's cubit A, as in his own book, *Historical Metrology*, Berriman say that it is 25.06 inches or 636 mm, i.e. 2/π metre.

1728 inches / 140 = 123.42857

1.02857 x 12 = 12.38284

This is the common Greek foot in inches.

Multiply by 2: 24.68567 inches, the sacred cubit

Multiply by 7: 172.8= 12 x 12 x 12

## Conclusion

Together the Belgic foot, the Druisian foot and the Saxon foot reveal a sophisticated and interconnected web of metrological traditions that span across different cultures and eras. Flinders Petrie's assertion that the Belgic foot forms the basis of modern English land measures highlights the enduring influence of pre-Roman measurement systems in Europe. His observation about the near-alignment of the ancient Germanic-British decimal system with the modern metric system underscores the potential for a seamless integration of historical and contemporary measures.

The Saxon foot, identified as a measure of 13.2 inches, connects ancient Babylonian, Sumerian, and Indus Valley metrology to the land measurement practices in medieval Europe. This unit's widespread historical use, from Mesopotamia to Neolithic Britain, illustrates the diffusion of measurement standards through trade, conquest, and cultural exchange.

The evidence suggests that various ancient units of measure, such as the Saxon foot and the Sumerian foot, may have shared common origins or influenced one another. This interconnectedness reflects a sophisticated understanding of geometry and a common metrological heritage that transcends regional boundaries.

## Notes

1. Flinders Petrie, M.W. 1911, "Weights and Measures", Encyclopædia Britannica 1911 Encyclopædia Britannica/Weights and Measures - Wikisource, the free online library

2. Ibid.

3. Ibid

4. Ibid

5. "Naming – “The first question which arises is the meaning of the name Fir Bolg. We may discard all “Belgic” and similar theories without discussion. We need not waste time over the “bags of earth” about which historians tell us. Kuno Meyer’s explanation (first given, so far as I know, in his Contributions to Irish Lexiocgraphy s.v. “bolg”) is by far the most reasonable: that Fir Bolg = Fir I mBolgaib (an expression used in poem no. XLIX quatrain 5) = bracati or breeches-wearers. Thus interpreted it becomes a term of contempt for the “lower orders.” “Now they were called Fir Bolg from the bags of clay which they used to place upon the bare rock-flags; and Fir Domnann from the deepening of the clay upon the bare rock-flags: and Gaileoin from the javelins of wounding that they had, as they were digging the clay. Or they were called Fir Bolg because they obtained a noisome territory in Greece from the King of Greeks, full of venomous reptiles, and the protection against the reptiles which they made was to carry with them clay of Ireland in bags: so that they were Fir Bolg, from the bags of clay which they carried with them in their canoes.” “This is why they are called Fir Bolg, for they used to carry clay with them from Ireland to sell to the Greeks for gold and for silver, in order to roof the cities. For there were venomous poisonous serpents and hurtful reptiles in those cities among the Greeks; and that is the real truth of the reason why they are called “Fir Bolg.” “The numerous explanations of the name Fir Bolg show that the expression had ceased to have any meaning when our history was compiled.” (source: Macalister, LGE, Vol. 3, p. 147, 153, 179, 193; Vol. 4, p. 2, 17, 31, 85)", LEBOR GABÁLA ÉRENN The Book of the Taking of Ireland PART VI Index O-P EDITED AND TRANSLATED WITH NOTES, ETC. BY R. A. Stewart Macalister, D.Litt. Microsoft Word - LGE - O-P.doc (ucc.ie)

6. Neal, John, August 06, 2003, post on Graham Hancock Message Board,

7. Neal, John, July 2003, "Ancient measurement systems: Their fractional integration", Author of the Month on Graham Hancock website, Ancient Measurement Systems: Their fractional integration - Graham Hancock Official Website

8. Ibid

9. Fréret, M, 1756, Essai, sur les Mesures Longues des anciens, Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son establissement jusqu'à présent, avec les Mémoires de Littérature tires des registres de cette Académie, depuis son renouvellement jusqu'en MDCCX, Volume 24, l'Imprimerie Royale

10. Alison, Jim, 2023, Babylonian and Roman Lengths, Volumes and Weights, C:\art\216art5.wpd (hiwaay.net)

11.Skinner F.G., 1952, The English Yard and Pound Weight. *Bulletin of the British Society for the History of Science*, *1*(7), 179–187. http://www.jstor.org/stable/4024847

## Bibliography

Alison, Jim, 2023, "Babylonian and Roman Lengths, Volumes and Weights" C:\art\216art5.wpd (hiwaay.net)

Fréret, M, 1756, Essai, sur les Mesures Longues des anciens, Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son establissement jusqu'à présent, avec les Mémoires de Littérature tires des registres de cette Académie, depuis son renouvellement jusqu'en MDCCX, Volume 24, l'Imprimerie Royale. Histoire de l'Academie Royale des Inscriptions et Belles-Lettres, depuis son ... - Google Books

LEBOR GABÁLA ÉRENN The Book of the Taking of Ireland PART VI Index O-P EDITED AND TRANSLATED WITH NOTES, ETC. BY R. A. Stewart Macalister, D.Litt. Microsoft Word - LGE - O-P.doc (ucc.ie)

Barthèlemy, Daniel and Dubois, Stéphane, 2007, Métrologie antique : Une tige métallique graduée découverte à Mâcon (Saône-et-Loire), Revue Archéologique de l'Est, tome 56. https://www.academia.edu/en/3768949/BARTHELEMY_D_DUBOIS_S_M%C3%A9trologie_antique_Une_tige_m%C3%A9tallique_gradu%C3%A9e_d%C3%A9couverte_%C3%A0_M%C3%A2con_Sa%C3%B4ne_et_Loire_2007

Berriman, Algernon Edward, 1953, *Historical Metrology: A New Analysis of the Archaeological and the Historical Evidence Relating to Weights and Measures,* Dent

Flinders Petrie, M.W. 1911, "Weights and Measures", Encyclopædia Britannica 1911 Encyclopædia Britannica/Weights and Measures - Wikisource, the free online library

Neal, John, August 06, 2003, post on Graham Hancock Message Board,

Neal, John, July 2003, "Ancient measurement systems: Their fractional integration", Author of the Month on Graham Hancock website, Ancient Measurement Systems: Their fractional integration - Graham Hancock Official Website

Newton. Isaac, 1737, A Dissertation upon the Sacred Cubit of the Jews and the Cubits of the several Nations, in John Greaves, *Miscellaneous Works of Mr. John Greaves, Professor of Astronomy in the University of Oxford*, vol. 2 (London: 1737), pp. 405-433.

Wakefield, Jim, "From the Rollrights to Stonehenge"

Skinner F.G., 1952, The English Yard and Pound Weight. *Bulletin of the British Society for the History of Science*, *1*(7), 179–187. http://www.jstor.org/stable/4024847

I like that you have identified the full hand as 4 inches 15840 in a mile.

This unit could easily be 13.333 imperial inches as 13.2 x100/99

It does work with the English acre

13.33333 x 13.33333 = 177.77777777777777777 square inches

The acre in sq inches is 522720 so dividing gives 2940.3 and by 3 gives 980.1 which is 99 x 99

In a mile there are 4752 / 80 = 59.4 x 13.333 = 792 one english chain so nothing actaully happens to the underlying measures and the imperial system base 99 become base 100

63360/99 = 640 very Egyptian.

So perhaps the Belgic foot is a phantom offshoot of the Sumerian and actually nothing changes, it is business as usual.

4752/2 = 2376 / 2 = 1188 and 11.88 inches is in Berriman's table…

Amazing work Melissa